Problem: The geometric sequence $(a_i)$ is defined by the formula: $a_i = -5 \left(2\right)^{i - 1}$ What is $a_{3}$, the third term in the sequence?
Answer: From the given formula, we can see that the first term of the sequence is $-5$ and the common ratio is $2$ To find $a_{3}$ , we can simply substitute $i = 3$ into the given formula. Therefore, the third term is equal to $a_{3} = -5 \left(2\right)^{3 - 1} = -20$.